SOLUTION: Question: Solve and round to the nearest hundredth. 7^x+2-4=136.

Question 201513: Question: Solve and round to the nearest hundredth. 7^x+2-4=136.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I assume the problem is to solve:

To start with, add 4 to both sides giving

Next, since 140 is not a power of 7 (it is a multiple but not a power), we will need to use logarithms. Use base 10 logarithms or natural logarithms, it doesn't matter. I will use base 10:

The is approximately 2.146128 so now we have

Using a property of logarithms () we get

Dividing by log(7) we get

The log(7) is approximately 0.845098 giving us

Subtracting 2 from both sides we get (rounded to the nearest hundredth):
x = 0.56
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